If a jewish person were to accidentally turn on the light in their bedroom, or if the television were accidentally turned on (for these purposes, let's assume that the person in question woke up, temporarily forgot what day it was, and turned on the electrical appliance), would the jew be allowed to benefit from the new situation (e.g. they can now read in their bedroom, or watch the single channel on TV). Leaving aside if someone else were to see the jewish person using this new situation (for this question, the person is living in an apartment, so nobody can look in and see what he's doing in his bedroom or living room), are there any halachic ramifications for benefiting from the new situation? Or must the jew simply 'ignore' the new situation and act like it doesn't exist?

As a side question, would it matter if the electrical appliance were turned on by a non-jew or a minor? I know a few times a shul had no lights on, and had to use a non-jew to turn on the lights as a 'loophole' to get the lights on; would they also be able to benefit from this?

Most authorities hold that television isn't "Shabbosdik", meaning that it is inappropriate to watch it on Shabbath even if it was left on since Friday. I think the question can be asked better from the angle of the light (as in your first example) or, for example, opening a refrigerator whose light then goes on (can you take food out of the refrigerator then?).
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Seth JFeb 27 '12 at 17:22

@SethJ What does the light being on have to do with taking the food out?
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Double AA♦Feb 27 '12 at 18:01

@DoubleAA, it helps you see inside, especially in the back, just like turning a light on in the room.
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Seth JFeb 27 '12 at 19:43

@SethJ That's fine but then it is equivalent to the light case. I though you were saying something about not benefiting from the open door as its opening caused an issur.
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Double AA♦Feb 27 '12 at 19:47

2 Answers
2

One may not ask a gentile to turn on one's oven or stove to heat food
on Shabbat, even if he will otherwise have no hot food for his Shabbat
meal. If a non-Jew does turn on the appliance to heat the food, one
may not partake of the food until after it once again cools, and one
who asks a gentile to turn on the appliance may not partake of the
food at all, even after it has cooled.

a. If a Jew directed a goy to do a D'Orysa Melacha on Shabbos, the
prohibition of benefit is so severe, that if, for instance the goy
turned on a light, the Jew must leave the room so as not to derive
pleasure from the Melacha .

b. If the goy did the Melacha d'Orysa without being asked, but did so
for the benefit of a Jew, then the Jew must protest.If he did not
protest, the Jew may derive indirect benefit from the Melacha ; i.e.,
carry on a conversation by the light, but not read thereby.

c. If the goy did not heed the protest, and nevertheless turned on the
light, the Jew may even read thereby.

d. Similarly, if a goy cooked food for a Jew on Shabbos, that food is
muktzeh and no Jew may partake of it until until enough time to have
completed that Melacha if it had been begun after Shabbos has elapsed
[bekedai she ya aseh].

In terms of deriving benefit from the actions done by a Jew on Shabbat the Shulchan Aruch (OC 318:1 and Mishna Berurah and Biur Halacha there) distinguish between a number of cases:

If a biblical prohibition was violated purposefully (deoraita bemeizid) then no one can derive benefit from it for the rest of shabbat, and the violator himself cannot derive benefit forever.

If a biblical prohibition was violated accidentally (deoraita beshogeg) then no one including himself can derive benefit from it for the rest of shabbat and everyone is permitted to derive benefit after shabbat. (Some are lenient here in a case of need.)

If a rabbinic prohibition was violated purposefully (derabanan bemeizid) then no one including himself can derive benefit from it for the rest of shabbat and everyone is permitted to derive benefit after shabbat. (Some question this ruling and forbid him from deriving benefit from it forever.)

If a rabbinic prohibition was violated accidentally (derabanan beshogeg) then it is permitted to all to benefit immediately.

A caveat:

Some hold that the above is true if violating the prohibition changed the object physically, but if something was carried between domains illegally then it remains permitted. Others dispute this distinction.

As for your case of electricity, this would very much depend on Why can't electricity be manipulated on Shabbat? If the electric appliance in question is a biblical prohibition then one would not be able to derive benefit for the remainder of shabbat, while if it is a rabbinic prohibition then one would be permitted to do so, as all of your cases seem to be shogeg.

[I note that I once heard a Rabbi argue that mindlessly turning on a light on shabbat is categorized as mitaseik not shogeg (a lower level of intention) but he was doing so in the context of the obligation for a korban so I hesitate to extend his chiddush to here. If others have seen this inside please let me know in the comments.]

In terms of your side question about non-Jews, I refer you to @GershonGold's answer.

Re mis'asek vs. shogeg: The question specifies "let's assume that the person in question woke up, temporarily forgot what day it was, and turned on the electrical appliance". That sounds like a classic case of shogeg. The case I've heard described as mis'asek is that someone arose and unthinkingly (out of habit because he was entering the room) stuck his hand out and turned on the light.
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msh210♦Feb 28 '12 at 5:36

@msh210 The question's examples also clearly don't involve carrying. (My answer was broader than the question's specific examples.) Do you have a source for this discussion inside? Also, have you heard it applied to maaseh shabbat issues?
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Double AA♦Feb 28 '12 at 16:55